Networks

How do social networks evolve?

• When new users join e.g. Twitter / Instagram, who do they follow?

• Celebrities? Politicians?

• Accounts related to the interests of the users

• Those with a huge following are more likely to be followed

Mathematical modelling

• To describe the phenomenon

• To capture the essence of the data

• Based on rules in mathematics and/or physics

• Simulate data and compare to real-life observations

Preferential attachment model

• Barabási and Albert (1999, Science)

• Rule 1: New nodes join the network one by one

• Rule 2: Each new node brings in (approximately) the same number of new edges

• Rule 3: Probability that an existing node gets an edge is proportional to their current degree

• Degree = number of edges

A simple example

A simple example

Adding the edges

Adding the edges

The process can keep going

Growing a big(ger) network

Distribution of the degree

On logarithmic scale

Bigger networks, more simulations

The power law

• The rich get richer (and the poor get poorer)

• The 80-20 rule / Pareto principle

• Cumulative inequality / disadvantage

• The Matthew effect (of accumulated advantage)

Takeaway

• The big picture stays the same

• Which individual nodes will succeed may vary

• Change involves an element of chance

Thank you for listening!